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Thomas Dehaeze
2024-12-17 15:37:17 +01:00
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content/article/oomen18_advan_motion_contr_precis_mechat.md
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Control of positioning systems is traditionally simplified by an excellent mechanical design.
In particular, the mechanical design is such that the system is stiff and highly reproducible.
In conjunction with moderate performance requirements, the control bandwidth is well-below the resonance frequency of the flexible mechanics as is shown in Figure [1](#figure--fig:oomen18-next-gen-loop-gain) (a).
In conjunction with moderate performance requirements, the control bandwidth is well-below the resonance frequency of the flexible mechanics as is shown in [Figure 1](#figure--fig:oomen18-next-gen-loop-gain) (a).
As a result, the system can often be completely **decoupled** in the frequency range relevant for control.
Consequently, the control design is divided into well-manageable SISO control loops.
Although motion control design is well developed, presently available techniques mainly apply to positioning systems that behave as a rigid body in the relevant frequency range.
On one hand, increasing performance requirements hamper the validity of this assumption, since the bandwidth has to increase, leading to flexible dynamics in the cross-over region, see Figure [1](#figure--fig:oomen18-next-gen-loop-gain) (b).
On one hand, increasing performance requirements hamper the validity of this assumption, since the bandwidth has to increase, leading to flexible dynamics in the cross-over region, see [Figure 1](#figure--fig:oomen18-next-gen-loop-gain) (b).
<a id="figure--fig:oomen18-next-gen-loop-gain"></a>
@@ -55,7 +55,7 @@ In this case, matrices \\(T\_u\\) and \\(T\_y\\) can be selected such that:
G = T\_y G\_m T\_u = \frac{1}{s^2} I\_{n\_{RB}} + G\_{\text{flex}}
\end{equation}
A tradition motion control architecture is shown in Figure [2](#figure--fig:oomen18-control-architecture).
A tradition motion control architecture is shown in [Figure 2](#figure--fig:oomen18-control-architecture).
<a id="figure--fig:oomen18-control-architecture"></a>
@@ -119,7 +119,7 @@ This leads to several challenges for motion control design:
A generalized plant framework allows for a systematic way to address the future challenges in advanced motion control.
The generalized plant is depicted in Figure [3](#figure--fig:oomen18-generalized-plant):
The generalized plant is depicted in [Figure 3](#figure--fig:oomen18-generalized-plant):
- \\(z\\) are the performance variables
- \\(y\\) and \\(u\\) are the measured variables and measured variables, respectively
@@ -180,8 +180,6 @@ This motivates a robust control design, where the **model quality is explicitly
## Feedforward and learning {#feedforward-and-learning}
## References
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
<div class="csl-entry"><a id="citeproc_bib_item_1"></a>Oomen, Tom. 2018. “Advanced Motion Control for Precision Mechatronics: Control, Identification, and Learning of Complex Systems.” <i>Ieej Journal of Industry Applications</i> 7 (2): 127–40. doi:<a href="https://doi.org/10.1541/ieejjia.7.127">10.1541/ieejjia.7.127</a>.</div>
<div class="csl-entry"><a id="citeproc_bib_item_1"></a>Oomen, Tom. 2018. “Advanced Motion Control for Precision Mechatronics: Control, Identification, and Learning of Complex Systems.” <i>IEEJ Journal of Industry Applications</i> 7 (2): 127–40. doi:<a href="https://doi.org/10.1541/ieejjia.7.127">10.1541/ieejjia.7.127</a>.</div>
</div>